Icosahedral geometry

The discovery of polyhedral boranes and polyhedral heteroboranes, which contain at least one atom other than in the cage, initiated a new era in boron chemistry.1-4 Most commonly, of the three commercially available isomeric dicarba-closo-dodecaborane carboranes(l,2-, 1,7-, and 1,12-), the 1,2-isomer 1 has been used for functionalization and connection to organic molecules. The highly delocalized three-dimensional cage bonding that characterizes these carboranes provides extensive thermal and kinetic stabilization as well as photochemical stability in the ultraviolet and visible regions. The unusual icosahedral geometry of these species provides precise directional control of all exopolyhedral bonds. 

C2Bl0H -CH2CH(NH2)CO2H o-carborane moiety with icosahedral geometry... 

Polyhedra in these high coordination numbers are often necessarily irregular, but when all the ligands are identical, near-icosahedral geometries occur for the 12-coordinate [Pr(l,8-naphthyridine)6] + and [La(N03)6] ions in crystalline salts. It should also be remembered that the geometries discussed here are found in the solid state, but on dissolution in a solvent, where the influence of counter-ions is lessened, matters may be different (see the aqua ions. Sections 4.3.1 and 4.3.2). In principle, isomers are often possible, but because of the lability of lanthanide complexes they are very rarely observed. 

Steric considerations (interdonor atom repulsions) make coordination numbers of 10 or more difficult, so fewer examples are known and, moreover, small differences between different types of polyhedra make assignment of a particular geometry difficult. Most examples involve nitrate, either alone (Section 3.7.7), or in combination with other polydentate ligands such as crown ethers (Section 3.7.8). Near-icosahedral geometries are found for regular 12-coordinate complexes such as Pr(naph)6 + and Ln(N03)6. ... 

A cluster density of states of Niia, literally (not just formally) broadened by 0.2 eV, is presented in Figure 2a for the icosahedral geometry near the equilibrium structure. The general features are roughly similar to that derived from a spin-polarized band structure calculation of bulk nickel. Near the Fermi level a very high density of states of the minority spin is found, the d band of the... 

Pig. 6. The icosahedral geometry of [Bi2Hi2] where the solid spheres represent BH fragments. 

There s a lot of polyhedral chemistry in boranes, including icosahedral geometry, whieh is now even more important because of buckminster-... 

The Hiickel molecular orbital theory for non-planar conjugated organic molecules has been applied to study the electronic structure and properties of the proposed icosahedral geometry of C ). The results support the suggestion that C o may be the first example of a spherical aromatic molecule. The molecule is calculated to have a stable closed shell singlet ground electronic state. 

Carbaborane has distorted nn icosahedral geometry. Pt is 1.81 A above a non-planar C2B3 face... 

Detailed X-ray crystallographic results have been reported for 1,1-bis-(dimethylphenylphosphine) - 2, 4 - dimethyl - 2, 4 - dicarba - 1 - platina - closo -dodecaborane [Pt(Me2C2B9H9)(PMe2Ph)2]. The carbaborane unit has distorted icosahedral geometry, and carbon atoms at the 2- and 4-positions, with the Pt at the 1-position. The Pt atom is ca. 1.81 A above the C2B3 face. 

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